Plasma dynamically induced frequency shifts in high-order harmonic generation in nitrogen

Experiments and theoretical calculations on high-harmonic generation in nitrogen are presented in the regime of laser pulses of a 300-ps duration, where the plasma dynamics following the ionization of the medium plays a decisive role. The experiments are performed with ∼4-GW Ti:sapphire laser pulses, giving rise to fully saturated ionization. The shifts between the exact harmonic frequency in the extreme ultraviolet and the integer multiple of the fundamental frequency are caused by the self-phase modulation of the laser pulse due to the time-dependent free-electron density in the plasma generated in the focal zone. Well-calibrated atomic resonances in the extreme ultraviolet measured through absorption in a secondary gas jet are used as frequency markers in the extreme ultraviolet for the accurate determination of the sign and magnitude of the frequency shifts. A theoretical model including both plasma dynamics and harmonic generation from atoms and ions has previously been developed, and successfully applied to explain the frequency red shift observed in xenon [Phys. Rev. Lett. 96, 123904 (2006)]. The plasma-dynamical model is extended and applied to the results of the harmonic generation in nitrogen, fully explaining the observed harmonic frequency shifts in the 9th and 13th harmonic.